(Solved): The cell in the figure, \( \quad \) could be used to provide a measure of the \( \mathrm{pH} \) in ...

The cell in the figure, \( \quad \) could be used to provide a measure of the \( \mathrm{pH} \) in the cathode compartment. Calculate the \( \mathrm{pH} \) of the cathode compartment solution if the cell emf at \( 298 \mathrm{~K} \) is measured to be \( 0.620 \mathrm{~V} \) when \( \left[\mathrm{Zn}^{2+}\right]=0.27 \mathrm{M} \) and \( P_{\mathrm{H}_{2}}=0.89 \mathrm{~atm} \). Express your answer using two decimal places.